Authors

Campus Units

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

2006

Journal or Book Title

Journal of Algebra and Its Applications

Volume

5

Issue

1

First Page

77

Last Page

88

DOI

10.1142/S0219498806001594

Abstract

We determine the identities of degree ≤ 6 satisfied by the symmetric (Jordan) product a○b = ab + ba and the associator [a,b,c] = (ab)c - a(bc) in every nonassociative algebra. In addition to the commutative identity a○b = b○a we obtain one new identity in degree 4 and another new identity in degree 5. We demonstrate the existence of further new identities in degree 6. These identities define a variety of binary-ternary algebras which generalizes the variety of Jordan algebras in the same way that Akivis algebras generalize Lie algebras.

Comments

The electronic version of this article is published as "Identities relating the Jordan product and the associator in the free nonassociative algebra," Journal of Algebra and its Applications 5, no. 01 (2006): 77-88. doi:10.1142/S0219498806001594. http://www.worldscientific.com/. Posted with permission.